2. In the polar coordinate system, take = Alnr+ Cr², in which A and C are constants. (i) verify can be used as stress function or not? (ii) if it is, deduce the expressions for stress components. 10 1 0² 10 18² =-for-² + Xor + r²de² or ² ror r²d0² As knowing in 2D case: V4= σ, 1 dø 1 0² + ror r²d0² + dr rar dr.² a 1 dø dr r de + 6=0

Elements Of Electromagnetics
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2. In the polar coordinate system, take = Alnr+ Cr², in which A and C are constants. (i) verify can
be used as stress function or not?
(ii) if it is, deduce the expressions for stress components.
As knowing in 2D case: V4=
do X v²
1 0 1 0²
+
σ₁ ==
ror
r²d0²¹
σo
8² 1 a
+
+
dr.²
1 0²
2
ar² rar r²de²
Tre=-
1 ə
+
a (1 dø
ar r de
dr² rdr
+
1 8²
r² do²
Transcribed Image Text:2. In the polar coordinate system, take = Alnr+ Cr², in which A and C are constants. (i) verify can be used as stress function or not? (ii) if it is, deduce the expressions for stress components. As knowing in 2D case: V4= do X v² 1 0 1 0² + σ₁ == ror r²d0²¹ σo 8² 1 a + + dr.² 1 0² 2 ar² rar r²de² Tre=- 1 ə + a (1 dø ar r de dr² rdr + 1 8² r² do²
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